Benefits of in-vehicle consolidation in less
than truckload freight transportation
operations
Rodrigo Mesa-Arango
Satish Ukkusuri
20th International Symposium of Transportation and Traffic Theory
Noorwijk, Netherlands
July 2013
Outline
1.
2.
3.
4.
5.
6.
Introduction
Problem
Methodology
Numerical Results
Conclusion
Questions/Comments
2 / 28
1. Introduction
• Trucking: Important economic sector (1)
– US GDP:
• For hire transportation:
– Trucking:
– Air:
– Rail:
$ 14,499 billion dollars
$ 403 billion dollars
$ 116 billion dollars
$
63 billion dollars
$
15 billion dollars
• Externalities
- Emissions - Safety
- Congestion - Asset deterioration
• Mitigation: Increasing vehicle utilization(2)(3)(4)(5)
(1) U.S. Department of Transportation (2012). National transportation statistics
(2) Sathaye, et al, The Environmental Impacts of Logistics Systems and Options for Mitigation, 2006
(3) Organisation for Economic Co-Operation and Development. Delivering the Goods-21st Century Challenges to Urban Goods Transport. 2003.
(4) European Commission, Directorate-General for Energy and Transport. Urban Freight Transport and Logistics. European Communities. 2006.
(5) Transport for London. London Freight Plan – Sustainable Freight Distribution: A Plan for London. 2007.
3 / 28
1. Introduction
• Economic mechanism attractive for
consolidation?
• Combinatorial Auctions
– Successful implementations
(6)(7)(8)(9)(10):
- Home Depot Inc.
- Staples Inc.
- Wal-Mart Stores Inc.
- Reynolds Metal Company
- K-Mart Corporation
- Ford Motor company
- The Limited
- Compaq Computer Corporation
- Sears Logistics Services
(6) Elmaghraby, and Keskinocak. Combinatorial Auctions in Procurement. 2002.
(7) De Vries, and Vohra. Combinatorial Auctions: A Survey. 2003.
(8) Moore, et al. The Indispensable Role of Management Science in Centralizing Freight Operations at Reynolds Metals Company. 1991
(9) Porter, et al. The First Use of a Combined-Value Auction for Transportation Services. 2002.
(10) Sheffi, Y. Combinatorial Auctions in the Procurement of Transportation Services. 2004.
4 / 28
1. Introduction
• Combinatorial Auctions in Freight Transportation
Shipper
Winner
Determination
Problem
(11) (12)(13)(14)
(11) Caplice and Sheffi. Combinatorial Auctions for Truckload Transportation. 2006.
(12) Sandholm. Algorithm for Optimal Winner Determination in Combinatorial Auctions. 2002
(13) Abrache, et al. Combinatorial auctions. Annals of Operations Research. 2007
(14) Ma, et al. A Stochastic Programming Winner Determination Model for Truckload Procurement Under Shipment Uncertainty. 2010
5 / 28
1. Introduction
• Bidding advisory models
− Truckload (TL) operations(15)(16)(17)(18)(19)
• Direct movements
• Economies of scope(20)(21)(22)(23)
− Less-Than-Truckload (LTL) operations?
• Consolidated movements
• Economies of scope, scale, density(20)(21)(22)(23)
(15) Song, and Regan. Combinatorial Auctions for Transportation Service Procurement, The Carrier Perspective. 2003,
(16) Song, and Regan. Approximation Algorithms for the Bid Construction Problem in Combinatorial Auctions for the Procurement of Freight Transportation Contracts. 2005,
(17) Wang, and Xia. Combinatorial Bid Generation Problem for Transportation Service Procurement. 2005
(18) Lee, et al. A Carrier’s Optimal Bid Generation Problem in Combinatorial Auctions for Transportation Procurement. 2007
(19) Chang. Decision Support for Truckload Carriers in One-Shot Combinatorial Auctions. 2009
(20) Caplice, and Sheffi. Combinatorial Auctions for Truckload Transportation. 2006
(21) Caplice. An Optimization Based Bidding Process: A New Framework for Shipper-Carrier Relationship. 1996
(22) Jara-Diaz. Transportation Cost Functions: A Multiproducts Approach. 1981
(23) Jara-Diaz. Freight Transportation Multioutput Analysis. 1983
6 / 28
1. Introduction
• Routes, costs and prices…
7 / 28
1. Introduction
• Economies of scope [TL]
c12
(i )
1
2
h
c24
c41
4
(i )
c12
c34
(ii )
c23
1
3
4
(ii )
2
k
c41
c12
c24
c34
1
(iii)
c23
h
k
3
c41
2
c24
4
c34
c23
h
3
(iii)
8 / 28
1. Introduction
• Economies of consolidation (scale and density) [LTL]
c12
(i )
1
4
(ii )
2
h
c24
c41
(i )
c12
c34
c23
1
4
3
(ii )
2
k
c41
c12
c24
c34
1
(iii)
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k
3
c41
2
c24
4
c34
c23
h
3
(iii)
9 / 28
1. Introduction
• This research
– Show Benefits for carries
• In-vehicle consolidation
• Bidding construction
– Freight Transportation combinatorial auctions
– Use
• Multi-commodity one-to-one pick up and delivery
vehicle routing problem (m-PDVRP) to find optimal
LTL bundles.
– Compare against optimal bundles obtained for TL
carriers
10 / 28
2. Problem
• MIP Formulation for m-PDVRP (1/2)
min 

vV (i , j )A
 x
vV jN
x
jN
v
0j
x
jN
v
ji
 1; i  N '
v
ij
Objective fun: Minimize total traversing cost
Each node visited once
 1; v V
All vehicles are used
  xijv ; i  N ; v V
Vehicle flow conservation
x
iM jM
cij xijv
jN
v
ij
 M 1; M  N '; v V
xijv  {1,0}; i, j  N; v V
Sub-tour elimination
Binary variables
…
11 / 28
2. Problem
• MIP Formulation for m-PDVRP (2/2)
min 

vV (i , j )A
cij xijv
Objective fun: Minimize total traversing cost
…
 l
vV jN
ri ,v
ji
 pri ; r  N ; i  N '
Demand Satisfaction constraint (Deliveries)
is ,v
ij
 pis ; s  N ; i  N '
Demand Satisfaction constraint (Pickups)
 l
vV jN
l
jN
  lijrs,v ; i  N '; r, s  N \ i; v V
rs ,v
ji
 l
rN sN
Payload flow conservation
jN
rs ,v
ij
 xijv Q; i, j  N '; v V
Loads only on traversed links without exceeding
vehicle capacity
l1rsi ,v  0 and lirs1 ,v  0; i  N '; r, s  N \ i; v V
Vehicles leave the depot empty and return empty
lijrs,v  0; i  N , j  N , r  N , s  N , v V
Non-negative continuous variables
12 / 28
3. Methodology
• Branch-and-price(24)(25)
– Branch-and-bound
– Dantzig-Wolfe and Column generation
• Master Problem
• Sub - problem
(24) Barnhart, et al. 1998. Branch-and-price: Column generation for solving huge integer programs.
(25) Desaulniers, et al. 1998. A unified framework for deterministic time constrained vehicle routing and crew scheduling problems.
13 / 28
3.1 Branch-and-bound
• Branch-and-Bound
– Solve linear relaxation of IP
– Terminate (fathom) a node
• Infeasibility \ Bound \ Solution
– Branch
– Stop when all nodes are terminated
IP
Linear Relaxation
Branch-and-Price
– Dantzig Wolfe
Decomposition
– Column
Generation
LP0
LP1
LP2
14 / 28
3.2. Dantzig Wolfe dec. + col. gen.
• MIP has special structure appropriate for
decomposition
– Master Problem (MP)
•
•
•
•
Linear Program
Controls column generation process
Requests columns from the Sub problem
Integer variables are represented as convex combination
of the columns generated by the Sub problem
– Sub Problem
• Integer program
• Generates columns
– Set of integer variables with common structure
15 / 28
3.2. Dantzig Wolfe dec. + col. gen.
 x
vV jN
x
jN
v
0j
x
jN
v
ji
Each node visited once
 1; v V
All vehicles are used
  xijv ; i  N ; v V
Vehicle flow conservation
x
iM jM
 1; i  N '
v
ij
jN
v
ij
 M 1; M  N '; v V
xijv  {1,0}; i, j  N; v V
Sub-tour elimination
Binary variables
…
Convex combination
xijv   xijv (t ) t
VRP deployment (t)

tT
t
tT
1
t  0
16 / 28
3.2. Dantzig Wolfe dec. + col. gen.
• Examples of deployments of trucks
|V| = 1
0
|V| = 2
1
1
0
1
t=1
3
2
3
2
0
1
0
1
3
2
t=2
t=2
3
1
t=1
t=1
0
0
|V| = 3
2
3
2
3
2
0
1
0
1
t=3
t=3
3
2
3
2
17 / 28
3.2. Dantzig Wolfe dec. + col. gen.
• Master problem (MP): Generates t as needed
min  c 
Objective fun: Minimize total traversing cost
l
jN
tT
jN
is
ij
l
jN
 pri ; r  N ; i  N '
ri
ji
l
rs
ji
(MP)
Demand Satisfaction constraint (Deliveries)
 pis ; s  N ; i  N '
Demand Satisfaction constraint (Pickups)
  lijrs ; i  N '; r, s  N \ i
Payload flow conservation
 l
rN sN
t t
rs
ij
jN
 Q aijt t ; i, j  N '
tT
( ij )
Loads only on traversed links without exceeding
vehicle capacity
l  0 and lirs1  0; i  N '; r, s  N \ i
Vehicles leave the depot empty and return empty
lijrs  0; i  N , j  N , r  N , s  N
Non-negative continuous variables
l1rsi  0 and lirs1  0; i  N '; r, s  N \ i
Vehicles leave the depot empty and return empty
rs
1i

jN
t
1
t  0 t T
( 0 )
Convexity Constraint
Non-negativity
18 / 28
3.2. Dantzig Wolfe dec. + col. gen.
• Each Solution generates a column t, {x0j0,…,xi0v}, that
is associated with a variable t in the MP
c  min 
*
 c
vV ( i , j )A
 x
vV jN
x
jN
v
1j
x
jN
v
ji
  ij  xijv   0
 1; i  N '
v
ij
Objective fun: Minimize reduced cost
(Sub-P)
Each node visited once
 1; v V
All vehicles are used
  xijv ; i  N ; v V
Vehicle flow conservation
x
iM jM
ij
jN
v
ij
 M 1; M  N '; v V
xijv  {1,0}; i, j  N; v V
Sub-tour elimination
Binary variables
19 / 28
3.2. Branch-and-price
Root B&B Node (Active)
Solve MP
Update arcs and costs
Set Sub-P costs
Add new column to pool
Solve Sub-P
No
Column Generation
Yes
Select B&B node and set as inactive
Terminate node by infeasibility
Terminate node by bound
Terminate node by solution
Active
nodes?
Set node as inactive
No
Update incumbent
solution
Branch
B&B node (active)
Column Generation
B&B node (active)
Column Generation
Stop
20 / 28
3.3. Acceleration strategies
• Originally depth-first search
– Finding initial incumbent solution (upper bound): Time
consuming
• Strategy 1: Fast initial upper bound
• Strategy 2: Continuous increment to lower bound
– Strategy 1 replace Step 3 as follows
• Find branch-and-bound node with current lowest solution
and fathom it, repeat
21 / 28
4. Numerical Results
• Implementation
– Java
• Branch-and-Bound
• Interactions in Column Generation
– Set Sub-P
– Update MP
• Network Management
– Information/Updates: Nodes, Links, Tours
– ILOG CPLEX
• MP LP Solution
• Sub-P IP Solution
22 / 28
4. Numerical Results
Scenario 1
Scenario 2
1
1
10
2
20
10
5
2
20
20
0
0
4
1
7
10
10
5
4
3
Scenario 3
2
20
20
0
6
4
8
3
6
cij
0
1
2
3
4
5
6
7
8
3
0
1
2
3
4
5
6
7
8
99.0 3.0 7.0 5.0 1.0 1.0 7.0 5.0 3.0
3.0 99.0 3.0 7.0 5.0 1.0 5.0 1.0 7.0
7.0 3.0 99.0 3.0 7.0 5.0 1.0 1.0 5.0
5.0 7.0 3.0 99.0 3.0 7.0 1.0 5.0 1.0
1.0 5.0 7.0 3.0 99.0 3.0 5.0 7.0 1.0
1.0 1.0 5.0 7.0 3.0 99.0 7.0 3.0 5.0
7.0 5.0 1.0 1.0 5.0 7.0 99.0 3.0 3.0
5.0 1.0 1.0 5.0 7.0 3.0 3.0 99.0 7.0
3.0 7.0 5.0 1.0 1.0 5.0 3.0 7.0 99.0
23 / 28
4. Numerical Results (LTL)
Min.
Deployment
Cost
5
5
5
5
5
5
7
7
7
7
7
7
7
7
7
9
9
9
9
9
9
9
9
9
9
9
9
1
1
1
2
2
2
1
1
1
2
2
2
3
3
3
1
1
1
2
2
2
3
3
3
4
4
4
50
40
20
50
40
20
50
40
20
50
40
20
50
40
20
50
40
20
50
40
20
50
40
20
50
40
20
13
13
21
30
30
30
11
15
31
28
28
32
45
45
45
13
13
31
26
26
30
43
43
43
60
60
60
0-1-2-3-4-0
0-1-2-3-4-0
0-1-3-2-4-0
0-1-3-0-2-4-0
0-1-3-0-2-4-0
0-1-3-0-2-4-0
0-5-1-2-6-3-4-0
0-5-1-6-2-3-4-0
0-5-6-1-3-2-4-0
0-2-4-0-5-1-6-3-0
0-2-4-0-5-1-6-3-0
0-1-3-0-5-6-2-4-0
0-1-3-0-2-4-0-5-6-0
0-1-3-0-2-4-0-5-6-0
0-1-3-0-2-4-0-5-6-0
0-5-1-7-6-2-3-8-4-0
0-5-1-7-6-2-3-8-4-0
0-5-6-7-1-8-3-2-4-0
0-2-4-0-5-1-7-6-3-8-0
0-2-4-0-5-1-7-6-3-8-0
0-1-7-3-8-0-5-6-2-4-0
0-2-4-0-5-1-6-3-0-7-8-0
0-2-4-0-5-1-6-3-0-7-8-0
0-1-7-3-8-0-2-4-0-5-6-0
0-1-3-0-2-4-0-5-6-0-7-8-0
0-1-3-0-2-4-0-5-6-0-7-8-0
0-1-3-0-2-4-0-5-6-0-7-8-0
Time (sec)
Bundles
Deep-first
search
{(1,3),(2,4)}
0.203
{(1,3),(2,4)}
0.188
{(1,3),(2,4)}
1.640
{(1,3)},{(2,4)}
1.063
{(1,3)},{(2,4)}
1.094
{(1,3)},{(2,4)}
0.891
{(1,3),(2,4),(5,6)}
0.359
{(1,3),(2,4),(5,6)}
2.609
{(1,3),(2,4),(5,6)}
1.937
{(2,4)},{(1,3),(5,6)}
23.124
{(2,4)},{(1,3),(5,6)}
16.734
{(1,3)},{(2,4),(5,6)}
7.390
{(1,3)},{(2,4)},{(5,6)}
15.344
{(1,3)},{(2,4)},{(5,6)}
14.203
{(1,3)},{(2,4)},{(5,6)}
5.484
{(1,3),(2,4),(5,6),(7,8)}
19.203
{(1,3),(2,4),(5,6),(7,8)}
7.094
{(1,3),(2,4),(5,6),(7,8)}
53.312
{(2,4)},{(1,3),(5,6),(7,8)}
574.012
{(2,4)},{(1,3),(5,6),(7,8)}
383.779
{(1,3),(7,8)},{(5,6),(2,4)}
5.812
{(2,4)},{(1,3),(5,6)},{(7,8)}
2148.677
{(2,4)},{(1,3),(5,6)},{(7,8)}
1267.945
{(2,4)},{(1,3),(7,8)},{(5,6)}
205.436
{(1,3)},{(2,4)},{(5,6)},{(7,8)} 692.870
{(1,3)},{(2,4)},{(5,6)},{(7,8)} 503.496
{(1,3)},{(2,4)},{(5,6)},{(7,8)} 260.092
Strategy 1 Strategy 2
0.171
0.188
0.734
1.125
1.078
0.672
0.234
8.062
4.688
13.469
16.109
7.109
3.985
13.406
3.719
37.265
53.656
103.359
219.905
214.186
36.406
254.654
270.67
91.984
91.375
101.702
59.71
0.313
0.406
0.531
0.265
0.203
0.235
0.281
1.718
5.859
4.390
4.781
6.000
1.812
1.813
1.125
12.188
10.531
55.406
113.172
174.281
130.657
397.782
413.016
138.625
58.084
77.581
39.563
Gap (%)
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
24 / 28
4. Numerical Results
• TL + Scenario 3
Min. Cost Deployment
9
9
9
9
1
2
3
4
43
42
47
60
0-1-3-2-4-5-6-7-8-0
0-1-3-2-4-0-5-6-7-8-0
0-1-3-0-5-6-2-4-0-7-8-0
0-1-3-0-2-4-0-5-6-0-7-8-0
Bundles
Time (sec)
Gap (%)
{(1,3),(2,4),(5,6),(7,8)}
{(1,3),(2,4)},{(5,6),(7,8)}
{(1,3)},{(2,4),(5,6)},{(7,8)}
{(1,3)},{(2,4)},{(5,6)},{(7,8)}
14.000
25.266
113.172
78.188
0.00
0.00
0.00
0.00
• Comparison
LTL operation
No.
Bundle
Total
lanes Deployment
cost
LTL
{(1,3),(5,6),(7,8)}
3
0-5-1-7-6-3-8-0
11.00
LTL
{(1,3),(5,6)}
2
0-5-1-6-3-0
13.00
TL
{(1,3),(2,4)}
2
0-1-2-3-4-0
13.00
TL
{(5,6),(7,8)}
2
0-5-7-6-8-0
13.00
TL
{(5,6),(2,4)}
2
0-5-2-6-4-0
13.00
TL / LTL {(1,3),(2,4),(5,6),(7,8)} 4
0-5-1-7-6-2-3-8-4-0 13.00
TL / LTL {(1,3)}
1
0-1-3-0
15.00
TL / LTL {(2,4)}
1
0-2-4-0
15.00
TL / LTL {(5,6)}
1
0-5-6-0
15.00
TL / LTL {(7,8)}
1
0-7-8-0
15.00
Opt.
for
TL operation
Cost per
Total
Deployment
lane
cost
3.67
0-5-6-1-3-7-8-0
35.00
6.50
0-5-6-1-3-0
25.00
6.50
0-1-3-2-4-0
21.00
6.50
0-5-6-7-8-0
21.00
6.50
0-5-6-2-4-0
17.00
3.25
0-1-3-2-4-5-6-7-8-0 43.00
15.00
0-1-3-0
15.00
15.00
0-2-4-0
15.00
15.00
0-5-6-0
15.00
15.00
0-7-8-0
15.00
Cost per
lane
11.67
12.50
10.50
10.50
8.50
10.75
15.00
15.00
15.00
15.00
LTL
min
margin
24.01
12
8
8
4
30
0
0
0
0
25 / 28
5. Conclusion
• Research shows benefits of considering in-vehicle
consolidation (LTL) in the construction of bids
• Numerical results show that consolidated bids (LTL)
dominate non-consolidated ones (TL)
• LTL carriers can submit bids with prices that are less than
or equal to the costs of TL carriers
• Savings increase as the capacity of trucks increases
• Low transportation costs potentially reduce shipper
procurement cost
• In-vehicle consolidation (as defined in this research)
integrates the flexibility of TL (economies of scope) to the
economies of scales/density of LTL
26 / 28
5. Conclusion
• Future research
– Understanding the tradeoff between low price and delivery
times (as well as other attributes of the carrier) for shippers
• Econometric techniques
• Segmented pricing policies
– Acceleration of the solution methodology
• Parallel computing
• Hybrid-metaheuristics
– Consideration of stochastic demand
– Development of a robust biding advisory model that
incorporates these features.
– Analysis of positive/negative externalities associated to large
trucks at a macroscopic level
• Thank you!
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6. Questions - Comments
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